Lower disorder-order transition

An important step in developing the mean-field concept was done by Landau [8, 10]. Without discussing the relation between such fundamental quantities as disorder-order transitions and symmetry lowering, we just want to note here that his theory is based on thermodynamics and the derivation of the temperature dependence of the order parameter via the thermodynamic potential minimization (e.g., the free energy A(r),T)) which is a function of the order parameter. It is assumed that the function A(rj,T) is analytical in the parameter 77 and thus near the phase transition point could be expanded into the series in 77 usually it is a polynomial expansion with temperature-dependent coefficients. Despite the fact that such a thermodynamical approach differs from the original molecular field theory, they are quite similar conceptually. In particular, the r.h.s. of the equation of state for the pressure of gases or liquids and the external field in ferromagnetics, respectively, have the same polynomial form. 

According to this sequence, the monovalent cations Rb+, Cs+ and K+ induce the transition at lower temperatures. Unlike other polyelectrolytes, the disorder-order transition of K-carrageenan is also sensitive to the presence of iodide as a result of electrostatic repnilsion between the anion and the sulfate group of K-carrageenan without aggregation of double helices to form a gel network Because of this particular feature, the iodide ion has been used to study the mechanism of gelation of this polysaccharide (Slootmaekers et al., 1988 Viebke et al., 1995,1998 Meunier et al., 2001 Takemesa Nishinari, 2004). 

As mentioned above the disorder-order transition in aqueous dispersions of charged latex particles, in particular well characterized polystyrene latices, has been investigated extensively. These particles interact through screened Coulombic interactions, the range of which depends on the electrolyte concentration in the suspension medium. At very low electrolyte concentration (10 M or lower) the transition from the milky white (disordered) state to the iridescent (ordered) state may occur at volume fractions below 1%. This means that colloidal spheres in suspension can maintain themselves in a regular lattice structure even when the interparticle spacing is several diameters. 

Oscillatory Shear Rheometry of Microsphase-Separated Block Copolymers Exhibiting Lower Critical Disorder-Order Transition Behavior... 

LCDOT Lower critical disorder-order transition... 

The Ag (100) surface is of special scientific interest, since it reveals an order-disorder phase transition which is predicted to be second order, similar to tire two dimensional Ising model in magnetism [37]. In fact, tire steep intensity increase observed for potentials positive to - 0.76 V against Ag/AgCl for tire (1,0) reflection, which is forbidden by symmetry for tire clean Ag(lOO) surface, can be associated witli tire development of an ordered (V2 x V2)R45°-Br lattice, where tire bromine is located in tire fourfold hollow sites of tire underlying fee (100) surface tills stmcture is depicted in tlie lower right inset in figure C2.10.1 [15]. 

Ramirez et al (1970) discussed a metal-insulator transition as the temperature rises, which is first order with no crystal distortion. The essence of the model is—in our terminology—that a lower Hubbard band (or localized states) lies just below a conduction band. Then, as electrons are excited into the conduction band, their coupling with the moments lowers the Neel temperature. Thus the disordering of the spins with consequent increase of entropy is accelerated. Ramirez et al showed that a first-order transition to a degenerate gas in the conduction band, together with disordering of the moments, is possible. The entropy comes from the random direction of the moments, and the random positions of such atoms as have lost an electron. The results of Menth et al (1969) on the conductivity of SmB6 are discussed in these terms. 

A somewhat different nomenclature, Tmst, is sometimes used instead of Todt, where MST refers to microseparation transition. This nomenclature can be misleading, however, since microseparation of one type of block from another occurs gradually as the temperamre is lowered, and it is distinct from the ordering transition at which symmetry is broken and an ordered phase appears at a sharply defined temperamre. This is particularly true when the composition of one of the blocks is low ( S0.15), so that well-segregated, but disordered, spheres (or polymeric micelles ), and sometimes worms and vesicles, appear. Thus, we prefer to avoid the potentially misleading nomenclature Tmst- ... 

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